The major factors determining drug responses are the input and disposition rates controlling pharmacokinetics, drug distribution to the site of action (biophase), the mechanism of drug action in altering mediator or receptor level, and transduction processes. May improvements in quantitating pharmacologic responses came from our recognition that diverse pharmacodynamic effects can be characterized using a family of four basic (and extended) indirect response models. These (and most) models require analysis using differential equations which usually cannot be fully integrated. This project seeks to characterize and quantify the properties of drugs acting by diverse mechanisms. Specific aims include development of a compendium with comparison of the array of relevant mechanism-based PK/PD models, further development of indirect response models with a precursor compartment including the occurrence of feedback alterations; evolution of extended indirect lifespan models for application to natural cell responses including effects such as bone marrow stimulation and/or cytotoxicity; and the detailed characterization of non-linear and time- dependent transduction models which may be applied to numerous membrane receptor (e.g., G-protein) mediated responses. Advanced methods of calculus and stimulations will be employed to seek exact or approximate solutions or behaviors for these models to identify how the onset, extent, return, duration, AUC, and steady-stage of responses are controlled, to recovery parameters more easily from experimental data, and to discriminate among diverse models available to describe typical data, and to determine how to optimize drug dosing regimens. These efforts will yield insights, methods, and resources for understanding and quantitating the time course of drug responses as related to major mechanisms of action.